Regarding correction in the Code

#1

#include<bits/stdc++.h>

using namespace std;

int minSteps(int n , int dp[])
{

dp[0] = 0;
dp[1] = 0;
for (int i = 2; i <=n; ++i) {
    if(i%2==0)
    {
        dp[i] =min(dp[i/2] , dp[i-1]) + 1;
    }
    else if(i%3==0)
    {
        dp[i] = min(dp[i/3] , dp[i-1]) + 1;
    }
    else
    {
        dp[i] = dp[i-1] + 1;
    }
}
return dp[n];

}

int main() {

int n;
cin >> n;
int dp[10005] = {0};
cout<<minSteps(n, dp);

}

//What is wrong in the above code for minimum steps to one ? It is giving wrong answer for n = 30;

#2 
dp[i]=dp[i-1]+1;
if(i%2==0)dp[i]=min(dp[i],dp[i/2]+1);
if(i%3==0)dp[i]=min(dp[i],dp[i/3]+1);

This should be the correct way

#3

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